A $4\mathrm{.}00$ m length of lightweight string is wound around a uniform cylindrical spool of radius $0\mathrm{.}500$ m and

mass $2\mathrm{.}28$ kg $.$ The spool is mounted on an axle with negligible friction and is initially at rest. The string is

pulled from the spool with a constant acceleration of magnitude $2\mathrm{.}80$m$//$s$^(2).$

$($a$)$ How much work has been done on the spool $($in J$)$ when it reaches an angular speed of $6\mathrm{.}07$rad$//$s $?$

$($b$)$ How long $($in s$)$ does it take the spool to reach this angular speed?

$($c$)$ How much string is left on the spool $($in m $)$ when it reaches this angular speed?